In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = -14, pq = -51

Clearly,

3 – 17 = -14, 3 (-17) = -51

Therefore, split 14a as 3a – 17a

Therefore,

a² – 14a – 51 = a² + 3a – 17a – 51

= a (a + 3) – 17 (a + 3)

= (a – 17) (a + 3)